Finite Group DatabasebetaFinite Group Databasebeta| order | 37602 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #34037763⋊C2 |
| Fitting, socle, derived, Sylow | C2089 ⋊ C2×C9 |
| Hall | #34037763 ⋊ C2 |
| Hall | D2089 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C2089 | C2×C9 |
| prime radical | D2089⋊C3 | C3 |
| cosocle | C2089⋊C3 | C2×C3 |
| LCS | G ▷ C2089 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2089 |
Polycyclic presentation:
2,3^2,2089|b^3=c,d^a=d^2088,d^b=d^1521,d^c=d^826134 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37602, 8);